Is it possible to bake dynamic paint waves simulation as a black and white displacement map texture?
Dynamic Paint can output to different targets depending on the Format. In your example you're baking to Vertex weights. However, changing it to Image Sequence will give you a new Output panel that allows the output to be baked to a sequence of images :

Once stored as a series of images you can use an Image Texture node set to 'Image Sequence' to retrieve the data and use it to drive the Displacement.